Here’s my quick thoughts without doing any math or providing formulas.

More than one answer is possible depending on how one interprets “correctly detects the disease 95% of the time”

If you know the sensitivity (% correct in patients with known disease), specificity (% correct in patients known to not have disease) and disease prevalence (1:1000 in this example) you can answer the question.

But overall measures of diagnostic accuracy (% correct overall based on combining sensitivity and specificity) could reach 95% through different combinations of sensitivity and specificity.  The different combinations could lead to different results for your question (a measure of positive predictive value)

Brian S. Alper, MD, MSPH

Editor-in-Chief, DynaMed (www.ebscohost.com/dynamed)

From: Evidence based health (EBH) [mailto:[log in to unmask]] On Behalf Of Simon Hatcher
Sent: Wednesday, February 09, 2011 6:22 PM
To: [log in to unmask]
Subject: Question about screening and denominators

I had this discussion with a friend over a beer last night and we couldn't agree on the answer. Here's the scenario:

The incidence of a disease in a population is 1:1000

There is a test which correctly detects the disease 95%of the time

If I test positive with the test what is my risk of having the disease?

Be interested in any thoughts on the "correct" answer.

Cheers

Simon